Express your answer as a mixed number simplified to lowest terms. $7\dfrac{1}{5}-4\dfrac{7}{10} = {?}$
Solution: Find a common denominator for the fractions: $= {7\dfrac{2}{10}}-{4\dfrac{7}{10}}$ Convert ${7\dfrac{2}{10}}$ to ${6 + \dfrac{10}{10} + \dfrac{2}{10}}$ So the problem becomes: ${6\dfrac{12}{10}}-{4\dfrac{7}{10}}$ Separate the whole numbers from the fractional parts: $= {6} + {\dfrac{12}{10}} - {4} - {\dfrac{7}{10}}$ Bring the whole numbers together and the fractions together: $= {6} - {4} + {\dfrac{12}{10}} - {\dfrac{7}{10}}$ Subtract the whole numbers: $=2 + {\dfrac{12}{10}} - {\dfrac{7}{10}}$ Subtract the fractions: $= 2+\dfrac{5}{10}$ Combine the whole and fractional parts into a mixed number: $= 2\dfrac{5}{10}$ Simplify to lowest terms: $= 2\dfrac{1}{2}$